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7th International Conference on Research in Air Traffic, 2016
The Federal Aviation Administration uses traffic management initiatives to prevent excessive congestion of airspace resources. We present a method that would aid in the planning of traffic management initiatives by identifying a representative set of initiatives that have been run in the past. In a more general unsupervised learning context, this method could be used to identify a small set of data points that are representative of the entire data set.
Recommended citation: Estes AS, Lovell DJ (2016) Identifying representative traffic management initiatives. Proc. 7th International Conference on Research in Air Traffic, 2016, Philadelphia, PA.
12th USA/Europe Air Traffic Management R&D Seminar, 2017
Models are proposed to estimate the performance of Ground Delay Programs as air traffic management initiatives. We apply Random Forest and Gradient-Boosted Forest regression techniques within the context of Geographically Weighted Regression. We estimate both the mean and 90th percentile responses for two performance indicators: average arrival delay and the number of cancelled arrivals.
Recommended citation: Estes AS, Ball MO, Lovell DJ (2017) Identifying representative traffic management initiatives. Proc. 12th USA/Europe Air Traffic Management R&D Seminar, 2017, Seattle, WA.
Proc. 8th International Conference on Research in Air Traffic 2018, 2018
We consider the problem of selecting a set of parameters for a ground delay program so that the program achieves a vector of performance objectives similar that is similar to a target vector. This could be used to support consensus-based ground delay program planning. We propose a method that selects several potential candidates of vectors and we compare our method with a simple greedy algorithm. Our results indicate that our proposed method is able to provide multiple solutions that are closer to the efficient frontier than the greedy solution.
Recommended citation: Estes AS, Ball MO, Lovell DJ (2018) Selecting parameters in performance-based ground delay program planning. Proc. 8th International Conference on Research in Air Traffic, 2018, Barcelona.
Proc. 13th USA/Europe Air Traffic Management R&D Seminar 2019, 2019
In this paper, we identify two weaknesses in the design of the collaborative trajectory options program (CTOP) traffic management initiative. First, CTOP may issue excessive quantities of delay even when the parameters of the program are chosen correctly. Second, CTOP’s current design can discourage airlines from accurately disclosing trajectory options. We propose new mechanisms that address these design flaws. We also provide computational results that demonstrate that our proposed mechanisms would reduce delay costs and encourage greater participation in CTOP.
Recommended citation: Estes AS, Ball MO (2019) Alternative resource allocation mechanisms for the Collaborative Trajectory Options Program (CTOP). Proc. 13th USA/Europe Air Traffic Management R&D Seminar, 2019, Vienna.
We study an approach to regression that we call objective-aligned fitting, which is applicable when the regression model is used to predict uncertain parameters of some objective problem. Rather than minimizing a typical loss function, such as squared error, we approximately minimize the objective value of the resulting solutions to the nominal optimization problem. While previous work on objective-aligned fitting has tended to focus on uncertainty in the objective function, we consider the case in which the nominal optimization problem is a two-stage linear program with uncertainty in the right-hand side. We define the objective-aligned loss function for the problem and prove structural properties concerning this loss function. Since the objective-aligned loss function is generally non-convex, we develop a convex approximation. We propose a method for fitting a linear regression model to the convex approximation of the objective-aligned loss. Computational results indicate that this procedure can lead to higher-quality solutions than existing regression procedures.
Published in Panamerican Mathematical Journal, 2013
Recommended citation: Estes AS (2013) Discrete Calculus on Mixed Time Scales. Panamerican Mathematical Journal. 23(4):23-46.
Published in Journal of Theoretical Biology, 2014
The Levene mechanism to maintain genotypic polymorphism by opposing selection on genotypes in multiple niches was proposed 60 years ago, and yet no systems were found to satisfy the mechanism׳s rather restrictive conditions. Reported here is such an example that a wolf spider population lives in a habitat of mixed rocks and leafy litter for which the females are phenotypically indistinguishable and the males have two distinct phenotypes subject to opposing selection with respect to the substrates. Census data is best-fitted to a population genetics model of the Levene type. A majority of the best fit support polymorphism, with many fitted parameter values quantitatively consistent with various laboratory studies on two closely related species.
Recommended citation: Deng B, Estes AS, Grieb B, Richard D, Hinds B, Hebets E (2014) A male spider׳s ornamentation polymorphism maintained by opposing selection with two niches. Journal of Theoretical Biology. 357:103-111. https://doi.org/10.1016/j.jtbi.2014.05.001
Published in Transportation Research Record, 2017
This paper provides a model-based approach to planning ground delay programs. Previous research on automated planning of ground delay programs has involved the use of mathematical programming techniques. This paper proposes a data-driven method that models the problem of choosing a traffic management initiative by using the framework of the multiarmed bandit decision problem. This approach makes greater use of the available data, and suggestions made by this procedure can be shown along with data that informed the decision. This combination of tools allows decision makers to more easily evaluate suggested decisions. The paper also provides simulations of the procedure on the basis of data from Newark (New Jersey) International Airport to evaluate its effectiveness.
Recommended citation: Estes AS, Ball MO (2017) Data-Driven Planning for Ground Delay Programs. Transportation Research Record. 2603(1):13-20. https://doi.org/10.3141/2603-02
Unsupervised prototype reduction for data exploration and an application to air traffic management initiatives
Published in EURO Journal on Transportation and Logistics, 2018
We discuss a new approach to unsupervised learning and data exploration that involves summarizing a large data set using a small set of “representative” elements. These representatives may be presented to a user in order to provide intuition regarding the distribution of observations. Alternatively, these representatives can be used as cases for more detailed analysis. We call the problem of selecting the representatives the unsupervised prototype reduction problem. We discuss the KC-UPR method for this problem and compare it to other existing methods that may be applied to this problem. We propose a new type of distance measure that allows for more interpretable presentation of results from the KC-UPR method. We demonstrate how solutions from the unsupervised prototype reduction problem may be used to provide decision support for the planning of air traffic management initiatives, and we produce computational results that compare the effectiveness of several methods in this application. We also provide an example of how the KC-UPR method can be used for data exploration, using data from air traffic management initiatives at Newark Liberty International Airport.
Recommended citation: Estes AS, Lovell DJ, Ball MO (2018) Unsupervised prototype reduction for data exploration and an application to air traffic management initiatives. EURO Journal on Transportation and Logistics. 2603(1):1-44. https://doi.org/10.1007/s13676-018-0132-0
Equity and Strength in Stochastic Integer Programming Models for the Dynamic Single Airport Ground-Holding Problem
Published in Transportation Science, 2020
We study stochastic integer programming models for assigning delays to flights that are destined for an airport whose capacity has been impacted by poor weather or some other exogenous factor. In the existing literature, empirical evidence seemed to suggest that a proposed integer programming model had a strong formulation, but no existing theoretical results explained the observation. We apply recents results concerning the polyhedra of stochastic network flow problems to explain the strength of the existing model, and we propose a model whose size scales better with the number of flights in the problem and that preserves the strength of the existing model. Computational results are provided that demonstrate the benefits of the proposed model. Finally, we define a type of equity property that is satisfied by both models.
Recommended citation: Estes AS, Ball MO. Equity and Strength in Stochastic Integer Programming Models for the Dynamic Single Airport Ground-Holding Problem. To appear in Transportation Science.
Monge Properties, Optimal Greedy Policies, and Policy Improvement for the Dynamic Stochastic Transportation Problem
Published in INFORMS Journal on Computing, 2020
We consider a dynamic, stochastic extension to the transportation problem. For the deterministic problem, there are known necessary and sufficient conditions under which a greedy algorithm achieves the optimal solution. We define a distribution-free type of optimality and provide analogous necessary and sufficient conditions under which a greedy policy achieves this type of optimality in the dynamic, stochastic setting. These results are used to prove that a greedy algorithm is optimal when planning a type of air traffic management initiative. We also provide weaker conditions under which it is possible to strengthen an existing policy. These results can be applied to the problem of matching passengers with drivers in an on-demand taxi service. They specify conditions under which a passenger and driver should not be left unassigned.
Recommended citation: Estes AS, Ball MO. Monge Properties, Optimal Greedy Policies, and Policy Improvement for the Dynamic Stochastic Transportation Problem. To appear in INFORMS Journal on Computing.
Published in Transportation Science, 2020
In this paper, we define and investigate quantity-contingent auctions. Such auctions can be used when there exist multiple units of a single product and the value of a set of units depends on the total quantity sold. For example, a road network or airport will become congested as the number of users increases so that a permit for use becomes more valuable as the total number allocated decreases. A quantity-contingent auction determines both the number of items sold and an allocation of items to bidders. Since such auctions could be used by bidders to gain excessive market power we impose constraints limiting market power. We focus on auctions that allocate airport arrival and departure slots. We propose a continuous model and an integer programming model for the associated winner determination problem. Using these models, we perform computational experiments that lend insights into the properties of the quantity-contingent auction.
Recommended citation: Ball MO, Estes AS, Hansen M, Liu Y. Quantity-Contingent Auctions and Allocation of Airport Slots. To appear in Transportation Science.
Published in SIAM Journal on Optimization, 2020
We study a type of network flow problem that we call the minimum- cost F-graph flow problem. This problem generalizes the typical minimum-cost network flow problem by allowing the underlying network to be a directed hy- pergraph rather than a directed graph. This new problem is pertinent because it can be used to model network flow problems that occur in a dynamic, stochastic, environment. We formulate this problem as an integer program, and we study specifically the case where every node has at least one outgoing edge with no capacity constraint. We show that even with this restriction, the problem of finding an integral solution is NP-Hard. However, we can show that all of the inequality constraints of our formulation are either facet-defining or redundant.
Recommended citation: Estes AS, Ball MO. To appear in SIAM Journal of Optimization.
Data Exploration with Selection of Representative Regions: Formulation, Axioms, Methods, and Consistency
Published in Mathematics of Operations Research, 2020
We present a new type of unsupervised learning problem in which we find a small set of representative regions that approximates a larger dataset. These regions may be presented to a practitioner along with additional information in order to help the practitioner explore the data set. An advantage of this approach is that it does not rely on cluster structure of the data. We formally define this problem, and we present axioms that should be satisfied by functions that measure the quality of representatives. We provide a quality function that satisfies all of these axioms. Using this quality function, we construct two methods for finding representatives. We provide convergence results for a general class of methods, and we show that these results apply to several specific methods, including the two methods proposed in this paper. We provide an example of how representative regions may be used to explore a data set.
Recommended citation: Estes AS, Ball MO, Lovell DJ. To appear in Mathematics of Operations Research.
Undergraduate course, University 1, Department, 2014
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Workshop, University 1, Department, 2015
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